Let [math]a[/math], [math]b[/math], [math]x[/math], and [math]y[/math] be positive integers with [math]a,b>1[/math]. Then the equation [math]x^a-y^b=1[/math] has only one solution set, namely [math]x=3[/math], [math]y=2[/math], [math]a=2[/math], and [math]b=3[/math]. This was conjectured by Eugène Charles Catalan in 1844 and was t...
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